Explicit Models for Threefolds Fibred by K3 Surfaces of Degree Two
Abstract
We consider threefolds that admit a fibration by K3 surfaces over a nonsingular curve, equipped with a divisorial sheaf that defines a polarisation of degree two on the general fibre. Under certain assumptions on the threefold we show that its relative log canonical model exists and can be explicitly reconstructed from a small set of data determined by the original fibration. Finally we prove a converse to the above statement: under certain assumptions, any such set of data determines a threefold that arises as the relative log canonical model of a threefold admitting a fibration by K3 surfaces of degree two.
Cite
@article{arxiv.1101.4763,
title = {Explicit Models for Threefolds Fibred by K3 Surfaces of Degree Two},
author = {Alan Thompson},
journal= {arXiv preprint arXiv:1101.4763},
year = {2019}
}
Comments
Early sections have been restructured and shortened. Assumptions required for the main construction have been weakened. Final version, accepted for publication by the Canadian Journal of Mathematics